It's all dependent on the one resistor that's on the board. Depending on the resister it can be from 10's mA to 1 Amp (which on the normal TP modules with just 1 IC, is the max)

Note: Julian Ilett did a test of the multi-IC versions that "supposedly" can charge up to 4 Amps (these boards were designed to charge 4 cells in parallel). In his findings, due to the variances in the IC's, they will not Start/Stop at the same time. And for this reason, they will over heat as they are kinda shorting each other out. (a diode stopping current/voltage will heat up)
So, in the end it's better to get 4 TP's and connect each one to its own cell, or just charge at 1 Amp to 4 cells each getting ~250 mA.